The Capital Asset Pricing Model is a financial model that assumes returns on a portfolio are normally distributed. Suppose a portfolio has an average annual return of 12.9% (i. e. an average gain of 12.9%) with a standard deviation of 22%. A return of 0% means the value of the portfolio doesn't change, a negative return means that the portfolio loses money, and a positive return means that the portfolio gains money.

(a) What percent of years does this portfolio lose money, i. e. have a return less than 0%
(b) What is the cutoff for the highest 15% of annual returns with this portfolio

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

and?

step-by-step explanation:

option (a)

step-by-step explanation:

step 1:   take 2 number whose product equal to 25..

and sum of those two number are -10

step: 2 for example here if we take 5,5 are the number,,

5*5=25

and

5+5=10

but we need -10

so if we take   -5,-5

so -5*-5=25

and -5+(-5)=-10

s0

come the equation

replace -10x by these number

like -5x -5x+25

take common

x(x-5)-5(x-5)=0

(x-5)(x-5)=0